Question

Cubical boxes of volume $15625c{m^3}$ each are put in a cubical store of side $2.5m$
I) How many such boxes can be put in the stores?
II) What are the dimensions of the box?
A) $(i)1250(ii)15cm$
B) $(i)1000(ii)15cm$
C) $(i)1250(ii)25cm$
D) $(i)1000(ii)25cm$

Answer 1

Hint: Here we will use some formula for calculating the number of boxes in given square feet and the dimensions of the box
for given questions. This two information is already given this question using formula and substitute the values and find the
answer.

Formula used: Dimension of box $ = {(side)^3}$
Number of boxes that store can contain $ = \dfrac{{{\text{Volume of cubical store}}}}{{{\text{Volume of 1 box}}}}$

Complete step-by-step solution:
In given in the question is
Volume of the boxes = $15625c{m^3}$
Side of cubical store $2.5m = 2.5 \times 100cm = 250cm$ (We will change the meter to centimeter we will multiply $100$ )
Volume of cubical store $ = {(side)^3} = {(250)^3} = 15625000c{m^3}$
Thus, number of boxes that store can contain $ = \dfrac{{{\text{Volume of cubical store}}}}{{{\text{Volume of 1 box}}}} =
\dfrac{{15625000}}{{15625}} = 1000$
Dimension of the box $ = 15625c{m^3}$
$
\Rightarrow sid{e^3} = 15625c{m^3} \\
\Rightarrow side = \sqrt[3]{{15625c{m^3}}} = \sqrt[3]{{25 \times 25 \times 25c{m^3}}} = 25cm
$
Side of the box is $ = 25cm$

Here the answer will be option D $1000,25cm$

Note: A cube is $3$ dimensional shape with $6$ equal sides, $6$ faces and $6$ vertices. Each face of a cube is a square. In $3$
dimension, the sides of a cube are, the length, width and the height. The volume of a solid cube is the amount of space
occupied by the solid cube. For a hollow cube, the volume is the difference in space occupied by the cube and amount of
space inside the cube.
Identify the length of side or length of the edge. Multiply the length by itself three times. Write the result accompanied by
the units of volume. Volume is measured in cubic units. Cubic meters $({m^3})$ ,cubic centimeters $(c{m^3})$ The volume
can also be measured in liters or milliliters.